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The socially stable core in structured transferable utility games

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  • Herings, P. Jean-Jacques
  • van der Laan, Gerard
  • Talman, Dolf

Abstract

We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on the set of players, for instance a hierarchical ordering or a dominance relation. The social structure is utilized to refine the core of the game, being the set of payoffs to the players that cannot be improved upon by any coalition of players. For every coalition the relative strength of a player within that coalition is induced by the social structure and is measured by a power function. We call a payoff vector socially stable if at the collection of coalitions that can attain it, all players have the same power.The socially stable core of the game consists of the core elements that are socially stable. In case the social structure is such that every player in a coalition has the same power, social stability reduces to balancedness and the socially stable core coincides with the core. We show that the socially stable core is non-empty if the game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and generically consists of a finite number of payoff vectors. Convex TU-games have a non-empty socially stable core, irrespective of the power function. When there is a clear hierarchy of players in terms of power, the socially stable core of a convex TU-game consists of exactly one element, an appropriately defined marginal vector. We demonstrate the usefulness of the concept of the socially stable core by two applications. One application concerns sequencing games and the other one the distribution of water.
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(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Herings, P. Jean-Jacques & van der Laan, Gerard & Talman, Dolf, 2007. "The socially stable core in structured transferable utility games," Games and Economic Behavior, Elsevier, vol. 59(1), pages 85-104, April.
  • Handle: RePEc:eee:gamebe:v:59:y:2007:i:1:p:85-104
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    References listed on IDEAS

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    1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2003. "Socially Structured Games and their Applications," Discussion Paper 2003-40, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    2. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
    3. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    4. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers 12-006/1, Tinbergen Institute.

    More about this item

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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